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Credit Default Simulator The credit default simulator is based on a simplified version credit risk methodology, extended to multiple periods. Beginning with a portfolio of assets, which are assumed to be in one-to-one correspondence with names, the model simulates a change in the value of the name for each period. Given a matrix of ratings transition probabilities, the changes in the valuations of each name are mapped into the matrix, which result in a simulated rating for each name in each period. Those names that default in period are identified, and the default loss for each period is computed according to the recovery rate assumptions. The extension to multiple periods is accomplished simply by generating a fresh value of from equation (1) for each name in each period. Of course, each name is mapped into the transition matrix using the rating with which it begins the period in question. However, a modification of equation (1) occurs for multiple periods if a feature of the model, known as the economic cycle, is activated. In this paper, we present generic models for valuing defaultable financial derivatives. For completeness, our study covers various cases: unilateral and bilateral, single payment and multiple payments, positive and negative payoffs. Although a couple of simple cases have been studied before by other authors, e.g. Duffie and Singleton (1999), Duffie and Huang (1996), who only provide heuristic derivations in a non-rigorous manner; analytic work on the other cases is novel. In contrast with the current recursive integral solution (see Duffie and Huang (1996)), our theory shows that the valuation of defaultable derivatives in most situations requires a backward induction procedure. Economic cycles are activated by specifying that a given value of is to be obtained over a user-input number of consecutive modeling periods. In the th period of an economic cycle, the value return is calculated according to The mapping of the value returns into the transition matrix is accomplished. Briefly, it consists of mapping the transition probabilities of the matrix into return value Z-score boundaries. If the simulated value return of a name crosses one of these Z-scores, a simulated transition event is generated. Let us consider a transition matrix , with different ratings. Then the probability of a name initially rated making a transition to rating is then given as The implied transitions feature of the model is assumed to be implemented in the following fashion. Associated with each asset in the portfolio to be modeled there is a credit spread. This credit spread is converted into a default probability according to the formula The model is designed to take into account credit enhancements in several forms. The first such form of enhancement is a subordinated tranche, which can be set to an arbitrary percentage of the total face value of the asset pool. The second type of enhancement is the excess spread. This is effectively a coupon on the remaining total face value of the pool which is paid into an account. The balance of this account is deducted from the total default losses in each period, and the excess spread account balance is reset. The third enhancement is the reserve account, which functions identically to the excess spread, except that payments to the reserve account stop when a specified maximum value is reached. References: |